Cosmological Redshift and Cosmic Time Dilation in the FLRW Metric

Abstract

The paper shows that the commonly used Friedmann-Lemaitre-Robertson-Walker (FLRW) metric describing the expanding Universe must be modified to properly predict the cosmological redshift. It is proved that the change in the frequency of redshifted photons is always connected with time dilation, similarly as for the gravitational redshift. Therefore, the cosmic time runs differently at high redshifts than at present. Consequently, the cosmological time must be identified with the conformal time and the standard FLRW metric must be substituted by its conformal version. The correctness of the proposed conformal metric is convincingly confirmed by Type Ia supernovae (SNe Ia) observations. The standard FLRW metric produces essential discrepancy with the SNe Ia observations called the ‘supernova dimming’, and dark energy has to be introduced to comply theoretical predictions with data. By contrast, the conformal FLRW metric fits data well with no need to introduce any new free parameter. Hence, the discovery of the supernova dimming actually revealed a failure of the FLRW metric and introducing dark energy was just an unsuccessful attempt to cope with the problem within this false metric. Obviously, adopting the conformal FLRW metric for describing the evolution of the Universe has many fundamental cosmological consequences.